Garreau et al. [1]} proposed to learn a distance metric
for measuring the similarity between two points. However, this method takes
the difference between the empirical alignment and true alignment as the
cost function. Therefore, it requires the true alignments among sequences,
which is not available for many real-world applications. Besides, it is only
feasible for multi-variate sequence alignment. Zhou et al. [2]} combined DTW with canonical correlation analysis
(CCA), termed canonical time warping (CTA). The point-wise distance is
linearly transformed by CCA. CTA alternatively optimizes the CCA and DTW
alignment to minimize the accumulative distance. However, CTA is only
applicable for multivariate sequences. The objective function of CTW is
non-convex and may return local minima.
